The Breakdown of Migdal's Theorem and the Divergence of Electron Polarizations in HTSC

We assume that Fermi surface nesting is a common feature in all oxide high temperature superconductors (HTSC) of perovskite or layered-perovskite structure. We show that this feature results in the breakdown of the Migdal's theorem, and the singularity of some electronic polarizations. These singularities trigger various kinds of instabilities in these materials.